Question

A melt containing 900 moles of anorthite and 100 moles of diopside undergoes crystallization. The number of moles of anorthite that crystallize as the melt composition moves from P to Q is .......... 

 

Hint:

In phase diagrams, the amount of a component that crystallizes can be determined by examining the change in composition as the melt cools.

Answer 1

Correct Answer: 800

Initial melt: 1000 moles total = 900 An + 100 Di → bulk composition = 90% An (point P).

On cooling from P to Q, only anorthite crystallizes (field: Anorthite + Melt).

At Q, the melt composition is 50% An (from the diagram).

Let L = moles of melt remaining at Q.

Anorthite mass balance:

\[900 = (\text{An in melt}) + (\text{An in solid})\]
\[900 = 0.5L + (1000 - L)\]
\[900 = 1000 - 0.5L \Rightarrow L = 200\]

So, anorthite crystallized:

\[1000 - 200 = \boxed{800 \text{ moles}}\]

The answer is 800 moles.